Question

After one side of the square was enlarged by 2 inches and the other side was enlarged by 3 inches area of the shape was doubled. What was the side of the square

Answer 1

Given:

After one side of the square was enlarged by 2 inches and the other side was enlarged by 3 inches area of the shape was doubled.

To find:

What was the side of the square?

Solution:

Let "s" represents the side of the square.

We know,

$\boxed{\bold{Area \:of\:a\:square = side^2}}$

So,

The area of the original square, A = s² . . . Equation 1

One side of the square was enlarged by 2 inches

∴ The new length of one side of the square will be = (s + 2) inches

and

The other side of the square was enlarged by 3 inches

∴ The new length of the other side of the square will be = (s + 3) inches

Now,

The new area of the square will be,

A' = (s + 2)(s + 3)

since the area of the square id doubled i.e., A' = 2A

⇒ 2A = (s + 2)(s + 3)

substituting from equation 1

⇒ 2s² = (s + 2)(s + 3)

⇒ 2s² = s² + 2s + 3s + 6

⇒ s² - 5s - 6 = 0

⇒ s² - 6s + s - 6 = 0

⇒ s(s - 6) + 1(s - 6) = 0

⇒ (s - 6)(s + 1) = 0

⇒ s = 6 or -1

since the length of the square cannot be negative

⇒ s = 6 inches

Thus, the side of the square is → 6 inches.

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